1). If r is not equal to one, show that a + ar + ar^2+ ....+ ar^n= a( r^n+1 -1)/( r-1).2). Establish the Bernoulli inequality: If 1+a>0, then ( 1+a)^n >= 1+na.3). 1^2+ 3^2+ 5^2 +...+ ( 2n-1)^2 = n ( 2n-1)(2n+1)/3

Q: Prove the inequality: P(A n B) ≥ 1 - P(A') - (B')   It reads: Probability of A intersect B is…

A: The inequality to be proved is : PA∩B≥1-PA'-PB' Proof: The PA∪B  is given as: PA∪B=PA+PB-PA∩B But…

Q: 2 ·Prove that at (xp ₁ %) the point of intersection of three confocals 2 ہے and he osculating plane…

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Q: O If fCos,y)=xty-xy%,find Joc-1,y-2. DIf 2=ea>c+ ky oflexx-by), Prove thet baz + ag = 2abz.

A: 1.Given function is fx,y=x3y-xy3. We have to find 1fx+1fy1,2

Q: n Rị |1-Ri Lecen (A) = II [A exp(-AZ,)]“ [exp(-ar)] z.)][exp(-Ar)]" i=1

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Q: Q2] Find the lower bound of Iz - 3|if |z - il < 1

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Q: C) If an expression is given that A+A'B'C=A+B'C, find the minimal expression of the function F =…

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Q: prove for all x,y in R^n: (1+||x+y||) ≥(1+||x||)/(1+||y||)

A: Sol:- The inequality to be proven is: (1 + ||x + y||) ≥ (1 + ||x||)/(1 + ||y||) Let's start by…

Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a&gt;0, n∈N and B=1+na

Q: What is the relative risk for the association between men and women vs COVID-19 infection? What do…

A: Data is given for Men and women, vs Covid infection ( Covid positive and Covid negative We have to…

Q: Suppose d(10!*x) = 2700, here x is another integer. What is the minimum possible value of x? Here…

A: given : Suppose d(10!*x) = 2700, here x is another integer and  gcd(10!, x) =1.

Q: Consider the set = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X Show that x₁ + x2 + x3 ≤ 2 is…

A: Here, in the question a set is given : X={x∈R4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4 ∈ {0, 1} } We…

Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

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Q: 1S) Solve coax=co 2x over [0,27) in saiana!

A: Explanation: Given that,                            We use the identity of cos2x…

Q: 1. 15x4- 13x²+ a is o(x*) . Hint: Apply theurem I.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1 Evaluate using Convolution theorem : L

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Q: Criven three points in R? x,=[-l,',2], [-1, !,2]", X, =-1,1,2]" and 1g=(-!,T,2]". Pind the %3D %3D…

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Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: Suppose Pr(A)=1/2, Pr(B)=1/4, and Pr(A v B)=1/2. What else can you say about A and B based on the…

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Q: For all a, b in R, show that -max{a^2, b^2} <ab max{a^2, b^2}.

A: To prove that for all (a,b)in(R), [max(−a2b2,ab)≤ab≤max(a2b2)] We'll consider three cases: 1.…

Q: let fai) = -x+7| -1-342| whare XER GIue Explietly expression for z y the full Bmupliyind

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Q: a) Prove the one point rule - 3-version: (3x)(x = t ^ A) = A[x = t] if x is not free in t. b) Prove…

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Q: sechx+cshx b) prove that e2x cshx-sechx

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Q: Prove that if AERnxm then rank(A) = rank(AT)

A: If A ∈ Rnxm then we have to prove that rank(A) = rank(AT)

Q: Since P+ Q, it follows that [(a1 + a3 + a5) – (a2 + a4)] [(B1 + B3 + B5) + A (82 + B4)]' | P+Q =…

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Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: lim G 5m-7 2m+4 o Show Transcribed Text without using hopital rule

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Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: 2. K42

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Hiw, Find radius and intervat fallowing po of Convergence 3. wer serier:

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Q: Show that the set A = {n^2/ (n+1): ne N} is unbounded in R.

A: To prove that the set A={n2n+1:n∈N} is unbounded in R,

Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: Let G = (a, b | a² = b4 = e, ab = b³a). a. Express a'b’abab³ in the form b'a', where 0 < is1 and…

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Q: + a3 + a5) – (@2 + đ4)I 4 [(a1 + a3 + as) – (a2 + a4)] [(B1 + B3 + B5) (a2 + a4) + A (B2 + Ba) (a1 +…

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Q: If P(B | A) > P(B), show that P(B' | A) P(B) + P(B' | A) > P(B) + P(B' | A) > P(B' | A) V > P(B' |…

A: Given P(B|A)&gt;P(B)We add P(B'|A) to both sidesP(B|A)+P(B'|A)&gt;P(B)+P(B'|A)1&gt;P(B)+P(B'|A)…